What’s Perception Got To Do with It? Re-framing Foundations for Rational Number Concepts

  • Percival G. MatthewsEmail author
  • Ryan Ziols
Part of the Research in Mathematics Education book series (RME)


Rational number knowledge is critical for mathematical literacy and academic success. However, despite considerable research efforts, rational numbers present perennial difficulties for a large number of learners. These difficulties have led some to posit that rational numbers are not a natural fit for human cognition. In this chapter, we challenge this assumption, describing recent research into intuitive routes to understanding rational number concepts that diverge from those popular in current curricular recommendations. Namely, we develop the claim that humans are perceptually sensitive to nonsymbolic ratio magnitudes, and that this sensitivity is an early developing, robust and abstract aspect of cognition. We suggest that attending to this perceptually based sensitivity can inform existing theory and help provide a basis for the design of more effective instruction on rational number concepts.


Rational numbers Perceptual learning Numerical cognition Perception Fractions 



Support for this research was provided in part by National Institutes of Health, project 1R03HD081087-01. The authors thank Brandon Singleton and Nicole Fonger for helpful commentary on an earlier draft of this manuscript.


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Authors and Affiliations

  1. 1.Department of Educational PsychologyUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of Curriculum and InstructionUniversity of Wisconsin-MadisonMadisonUSA

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